Modeling Quantum States with Broken Symmetries

Created by: chrisrothUT

We now have the models RBMSymm and GCNN that can learn the wavefunction of the lowest-lying symmetric energy level. As @attila-i-szabo and i discussed today, it would be really nice to be able to explore broken symmetry states as well. We need two things:

a) A layer that does a phase-weighted average over the output (pre-averaging) of a GCNN or RBMSymm using the desired character of the symmetry group. This should be straightforward to implement.

b) A method for generating the character of the symmetry group by specifying eigenvalues w.r.t to symmetry operations.( I.e. specify the character table for p4 by specifying R(\pi/4) and T(1,0) and T(0,1) )

There's a few ways to go about b).

We could try to make lattice (or graph) generate a labelled SymmGroup (this may or may not be useful [https://networkx.org/documentation/stable/reference/algorithms/isomorphism.ismags.html]) instead of randomly arranged isomorphisms. Any ideas @VolodyaCO?

We could also work with the algebraic group (instead of the graph) and try to generate the cosets from that. This may not produce the cosets we want, but we can still use it to look for valid character tables. This would require some work from the user to figure out what these character tables mean.